I bought Need for speed most wanted 2012 from the PSN Store on Friday November 23 2012 after trying the full game trial. When I bought it from the psn store a popup said that I would not need to redownload it that it would recognize that it was purchased. But it didn't the trial expired, so I deleted it and tried to redownload it from the store, only the store doesn't show that I purchased it at all and the only thing that shows up in my download list is the multilayer online pass for said game.
don't know how to do that either
Here's a more useful link.
Now for your problem. You won't be able to redownload the time trial but is there a demo? You'll need to download that. If not you may have "painted yourself into a corner" an need to contact Customer Service. There's a link at the bottom of this page or their number is 1-800-345-7669